Basic Concept of Electrostatics

 

 

Electric charges:
 Basic or fundamental particle of in electric field is called an electric charge. They are basically formed by the transfer of electron from the atom. They are two types i.e. positive and negative. Positive charges are formed by the loss and negative charges are formed by gain of electron.

Properties of charges:
The electric charges possess following properties:

i                     Charges are two types. Like charges repel each other and unlike charges attract each other.

ii                  Total charge of any system remains conserved. It means in a system charges neither created nor be destroyed but only can transfer.

iii               Charges are quantized quantity. It means total charge present on a system is always integer multiple times basic unit.

i.e. q = ne , where ‘n’ is an integer = 1,2,3,……

Method of charging a neutral body:

A body can be charged by three ways:

i                     Rubbing or friction: The process of developing charge on a neutral body by rubbing the surfaces. When two surfaces are rubbed against each other then one transfer electron to another and charges are produced.

For eg. A comb rubbed on dry hair attracts the dust particles.

 

ii                  Conduction: The process of developing charge on a neutral body with physical contact is called conduction. Here, charge body transfers its charge directly to the neutral body.

iii               Induction: The process of developing charge on a neutral body without physical contact is called induction. It works due to electrostatic force.

 

Surface charge density and action of points:

The charge stored in a body per unit area is called surface charge density.

i.e. σ = q/A

It measures the concentration of charge on a given surface. And smaller the surface area, high will be the concentration of charge and vice-versa.

i.e. σ α 1/A

Action of points: The leakage of charges through small surfaces area of a body is called action of points. Because of high concentration of charges in smaller area, they can easily leak out from sharp parts.

Coulomb’s law in electrostatics:

It states that “The force of attraction or repulsion between two charges is directly proportional to the product of their magnitude and inversely proportional to the square of distance between them. 

Consider, two charges of magnitude q1 and q2 are at a distance ‘r’ apart each oter. Then according to Coulomb’s law;

i.e. F α q₁q₂ …………..(i)

       F α 1/r² …………..(ii)

After combining equations (i) and (ii), we get

F α q₁q₂/r²

F = q₁q₂/4πε_or²

 

F = q₁q₂/4πε_or² …………(iii)

This is the electrostatic force between two charges. Where, ‘ε_o’ is the permittivity in free space or vacuum. Its value is 8.854x10^-12 C²N^-1m^-2.

Permittivity (ε):

The ability of medium to allow the electric field or electrostatic force is called permittivity of the medium. Its value depends upon nature of the medium. Its value is least in free space or vacuum ε_o= 8.854x10^-12 C²N^-1m^-2.

Relative permittivity is the ratio of permittivity in medium to the permittivity in vacuum. It is also called dielectric constant.

i.e. ε_r =ε/ε_o

Short questions:

Q1) Why sharp points are avoided in electrostatic machines?

Ans: Sharp points have low surface area and high surface charge density by the relation,

i.e σ = q/A or, σ α 1/A

Because of high concentration of charge sharp points easily leak out the charges through action of points. So, the efficiency of electrostatic machine decreases.

.^..Hence, to prevent the loss of charges from sharp points the electrostatic machine

Q2) The aeroplane have slightly conducting tyres to move on the runway, why?

Ans: When aeroplane moves on the runway then friction produced between the ground and tyres. The friction develops charges on the body. If the charges passes into the fuel tank that may cause firing or burning the aeroplane.

Therefore, to leak out the charges from the tyres into the ground, the aeroplane have conducting tyres.

Electrostatic induction:

The method of charging a body without physical contact is called electrostatic induction. By electrostatic induction we can charge a neutral body without physical contact.

 

Fig: How to make positive charge on a neutral body

 

Numerical:

Q 1) Calculate the value of two equal charges if they repel one another with the force of 0.1N when situated 50cm apart in vacuum. What would be the distance between them if they are placed in an insulating medium of dielectric constant 10?

Ans: Given that,

First charge (q₁) = x

Second charge (q₂) = x (Being equal charges)

Distance (r) = 50cm = 0.5m

Force (F) = 0.1N

We know that,

F = q₁q₂/4πε_or²

Or, 0.1 = 9x10⁹. x.x / (0.5)²       (1/4πε_o = 9x10⁹)

Or, 0.1x0.25 = 9x10⁹ . x²

Or, 0.025 = 9x10⁹. x²

Or, 2.78x10^-12 = x2

Or, x = √(𝟐.𝟕𝟖𝐱𝟏𝟎^−𝟏𝟐)

⸫ x = 1.67x10-6 C #

 

Second part;

If dielectric constant (ε_o) = 10

Or, ε /ε_o = 10

⸫ ε = 10 ε_o ………….(i)

Again, New force will be same but distance should be different. Let new distance is ‘R’.

F’ = q₁q₂/4πεR²

Or, F = q₁q₂/4π10 ε_oR²

Or, 0.1 = 1.67x10^-6x1.67x10^-6x9x10⁹/10R²

Or, 0.1 = 2.51x10^-3/R²

Or, R² = 25.1x10^-3

Or, R = √(𝟐𝟓.𝟏𝒙𝟏𝟎^−𝟑)

⸫ R = 0.158 m #